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Differential Geometry and its Applications
Article . 2022 . Peer-reviewed
License: Elsevier TDM
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2018
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
http://dx.doi.org/10.1016/j.di...
Article
License: Elsevier TDM
Data sources: Sygma
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H-type foliations

Authors: Baudoin, Fabrice; Grong, Erlend; Rizzi, Luca; Vega-Molino, Gianmarco;

H-type foliations

Abstract

With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound, we prove on those structures sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann, we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of those spaces in codimension more than 2.

accepted version

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), FOS: Mathematics, 510

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Average
Average
Average
Green